tan-example (used to crash)

Percentage Accurate: 78.7% → 99.7%

Time: 38.1s

Alternatives: 10

Speedup: 1.0×

Specification

\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x + \left(\frac{\frac{\sin y}{\cos y} + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (- (/ (+ (/ (sin y) (cos y)) (tan z)) (- 1.0 (* (tan z) (tan y)))) (tan a))))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	return x + ((((sin(y) / cos(y)) + tan(z)) / (1.0 - (tan(z) * tan(y)))) - tan(a));
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((((sin(y) / cos(y)) + tan(z)) / (1.0d0 - (tan(z) * tan(y)))) - tan(a))
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	return x + ((((Math.sin(y) / Math.cos(y)) + Math.tan(z)) / (1.0 - (Math.tan(z) * Math.tan(y)))) - Math.tan(a));
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	return x + ((((math.sin(y) / math.cos(y)) + math.tan(z)) / (1.0 - (math.tan(z) * math.tan(y)))) - math.tan(a))

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(Float64(sin(y) / cos(y)) + tan(z)) / Float64(1.0 - Float64(tan(z) * tan(y)))) - tan(a)))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, a)
	tmp = x + ((((sin(y) / cos(y)) + tan(z)) / (1.0 - (tan(z) * tan(y)))) - tan(a));
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[(N[Sin[y], $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. div-inv 99.6%

      \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

3. Applied egg-rr 99.6%

   \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
4. Step-by-step derivation

   1. associate-*r/ 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. *-rgt-identity 99.7%

      \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

5. Simplified 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
6. Step-by-step derivation

   1. tan-quot 99.6%

      \[\leadsto x + \left(\frac{\color{blue}{\frac{\sin y}{\cos y}} + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]

   2. div-inv 99.6%

      \[\leadsto x + \left(\frac{\color{blue}{\sin y \cdot \frac{1}{\cos y}} + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]

   3. fma-def 99.7%

      \[\leadsto x + \left(\frac{\color{blue}{\mathsf{fma}\left(\sin y, \frac{1}{\cos y}, \tan z\right)}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

7. Applied egg-rr 99.7%

   \[\leadsto x + \left(\frac{\color{blue}{\mathsf{fma}\left(\sin y, \frac{1}{\cos y}, \tan z\right)}}{1 - \tan y \cdot \tan z} - \tan a\right) \]
8. Step-by-step derivation

   1. fma-udef 99.6%

      \[\leadsto x + \left(\frac{\color{blue}{\sin y \cdot \frac{1}{\cos y} + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

   2. associate-*r/ 99.6%

      \[\leadsto x + \left(\frac{\color{blue}{\frac{\sin y \cdot 1}{\cos y}} + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]

   3. *-rgt-identity 99.6%

      \[\leadsto x + \left(\frac{\frac{\color{blue}{\sin y}}{\cos y} + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]

9. Simplified 99.6%

   \[\leadsto x + \left(\frac{\color{blue}{\frac{\sin y}{\cos y} + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

10. Final simplification 99.6%

    \[\leadsto x + \left(\frac{\frac{\sin y}{\cos y} + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \]

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := \tan z + \tan y\\ \mathbf{if}\;\tan a \leq -0.005 \lor \neg \left(\tan a \leq 0.00015\right):\\ \;\;\;\;\mathsf{fma}\left(t_0, 1, x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{1 - \tan z \cdot \tan y} + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan z) (tan y))))
   (if (or (<= (tan a) -0.005) (not (<= (tan a) 0.00015)))
     (fma t_0 1.0 (- x (tan a)))
     (+ (/ t_0 (- 1.0 (* (tan z) (tan y)))) (- x a)))))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	double t_0 = tan(z) + tan(y);
	double tmp;
	if ((tan(a) <= -0.005) || !(tan(a) <= 0.00015)) {
		tmp = fma(t_0, 1.0, (x - tan(a)));
	} else {
		tmp = (t_0 / (1.0 - (tan(z) * tan(y)))) + (x - a);
	}
	return tmp;
}

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	t_0 = Float64(tan(z) + tan(y))
	tmp = 0.0
	if ((tan(a) <= -0.005) || !(tan(a) <= 0.00015))
		tmp = fma(t_0, 1.0, Float64(x - tan(a)));
	else
		tmp = Float64(Float64(t_0 / Float64(1.0 - Float64(tan(z) * tan(y)))) + Float64(x - a));
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.005], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 0.00015]], $MachinePrecision]], N[(t$95$0 * 1.0 + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -0.0050000000000000001 or 1.49999999999999987e-4 < (tan.f64 a)

   1. Initial program 78.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Step-by-step derivation

      1. associate-+r- 77.8%

         \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

      2. +-commutative 77.8%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

      3. associate--l+ 77.9%

         \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]
   4. Step-by-step derivation

      1. add-cbrt-cube 77.5%

         \[\leadsto \tan \left(y + z\right) + \color{blue}{\sqrt[3]{\left(\left(x - \tan a\right) \cdot \left(x - \tan a\right)\right) \cdot \left(x - \tan a\right)}} \]

      2. pow3 77.5%

         \[\leadsto \tan \left(y + z\right) + \sqrt[3]{\color{blue}{{\left(x - \tan a\right)}^{3}}} \]

   5. Applied egg-rr 77.5%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\sqrt[3]{{\left(x - \tan a\right)}^{3}}} \]
   6. Step-by-step derivation

      1. tan-sum 98.8%

         \[\leadsto \color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} + \sqrt[3]{{\left(x - \tan a\right)}^{3}} \]

      2. rem-cbrt-cube 99.4%

         \[\leadsto \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \color{blue}{\left(x - \tan a\right)} \]

      3. div-inv 99.4%

         \[\leadsto \color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} + \left(x - \tan a\right) \]

      4. fma-def 99.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\tan y + \tan z, \frac{1}{1 - \tan y \cdot \tan z}, x - \tan a\right)} \]

      5. +-commutative 99.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\tan z + \tan y}, \frac{1}{1 - \tan y \cdot \tan z}, x - \tan a\right) \]

      6. *-commutative 99.4%

         \[\leadsto \mathsf{fma}\left(\tan z + \tan y, \frac{1}{1 - \color{blue}{\tan z \cdot \tan y}}, x - \tan a\right) \]

   7. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\tan z + \tan y, \frac{1}{1 - \tan z \cdot \tan y}, x - \tan a\right)} \]

   8. Taylor expanded in z around 0 78.3%

      \[\leadsto \mathsf{fma}\left(\tan z + \tan y, \frac{1}{\color{blue}{1}}, x - \tan a\right) \]

   if -0.0050000000000000001 < (tan.f64 a) < 1.49999999999999987e-4

   1. Initial program 78.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Step-by-step derivation

      1. associate-+r- 78.7%

         \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

      2. +-commutative 78.7%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

      3. associate--l+ 78.7%

         \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x + -1 \cdot a\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \left(x + \color{blue}{\left(-a\right)}\right) \]

      2. unsub-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]

   6. Simplified 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]
   7. Step-by-step derivation

      1. tan-sum 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. div-inv 99.8%

         \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   8. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} + \left(x - a\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. *-rgt-identity 99.8%

         \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

   10. Simplified 99.7%

       \[\leadsto \color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} + \left(x - a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005 \lor \neg \left(\tan a \leq 0.00015\right):\\ \;\;\;\;\mathsf{fma}\left(\tan z + \tan y, 1, x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} + \left(x - a\right)\\ \end{array} \]

Alternative 3: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \tan a\right) \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y)))) (tan a))))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	return x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - tan(a));
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(z) + tan(y)) / (1.0d0 - (tan(z) * tan(y)))) - tan(a))
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	return x + (((Math.tan(z) + Math.tan(y)) / (1.0 - (Math.tan(z) * Math.tan(y)))) - Math.tan(a));
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	return x + (((math.tan(z) + math.tan(y)) / (1.0 - (math.tan(z) * math.tan(y)))) - math.tan(a))

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(z) + tan(y)) / Float64(1.0 - Float64(tan(z) * tan(y)))) - tan(a)))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - tan(a));
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. div-inv 99.6%

      \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

3. Applied egg-rr 99.6%

   \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
4. Step-by-step derivation

   1. associate-*r/ 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. *-rgt-identity 99.7%

      \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

5. Simplified 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

6. Final simplification 99.7%

   \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \tan a\right) \]

Alternative 4: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005 \lor \neg \left(\tan a \leq 0.0002\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.005) (not (<= (tan a) 0.0002)))
   (+ x (- (tan y) (tan a)))
   (- (+ x (tan (+ y z))) a)))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.005) || !(tan(a) <= 0.0002)) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = (x + tan((y + z))) - a;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((tan(a) <= (-0.005d0)) .or. (.not. (tan(a) <= 0.0002d0))) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = (x + tan((y + z))) - a
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.005) || !(Math.tan(a) <= 0.0002)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = (x + Math.tan((y + z))) - a;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.005) or not (math.tan(a) <= 0.0002):
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = (x + math.tan((y + z))) - a
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.005) || !(tan(a) <= 0.0002))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.005) || ~((tan(a) <= 0.0002)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = (x + tan((y + z))) - a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.005], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 0.0002]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -0.0050000000000000001 or 2.0000000000000001e-4 < (tan.f64 a)

   1. Initial program 77.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 60.4%

      \[\leadsto \color{blue}{\left(x + \frac{\sin y}{\cos y}\right) - \frac{\sin a}{\cos a}} \]
   3. Step-by-step derivation

      1. tan-quot 60.4%

         \[\leadsto \left(x + \color{blue}{\tan y}\right) - \frac{\sin a}{\cos a} \]

      2. tan-quot 60.5%

         \[\leadsto \left(x + \tan y\right) - \color{blue}{\tan a} \]

      3. associate--l+ 60.5%

         \[\leadsto \color{blue}{x + \left(\tan y - \tan a\right)} \]

   4. Applied egg-rr 60.5%

      \[\leadsto \color{blue}{x + \left(\tan y - \tan a\right)} \]

   if -0.0050000000000000001 < (tan.f64 a) < 2.0000000000000001e-4

   1. Initial program 78.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Step-by-step derivation

      1. associate-+r- 78.8%

         \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

      2. +-commutative 78.8%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

      3. associate--l+ 78.8%

         \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x + -1 \cdot a\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \left(x + \color{blue}{\left(-a\right)}\right) \]

      2. unsub-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]

   6. Simplified 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]
   7. Step-by-step derivation

      1. associate-+r- 78.7%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right) - a} \]

   8. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right) - a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005 \lor \neg \left(\tan a \leq 0.0002\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \]

Alternative 5: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 0.0002:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;\tan y + \left(x - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -0.005)
   (+ x (- (tan y) (tan a)))
   (if (<= (tan a) 0.0002)
     (- (+ x (tan (+ y z))) a)
     (+ (tan y) (- x (tan a))))))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.005) {
		tmp = x + (tan(y) - tan(a));
	} else if (tan(a) <= 0.0002) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = tan(y) + (x - tan(a));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-0.005d0)) then
        tmp = x + (tan(y) - tan(a))
    else if (tan(a) <= 0.0002d0) then
        tmp = (x + tan((y + z))) - a
    else
        tmp = tan(y) + (x - tan(a))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -0.005) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else if (Math.tan(a) <= 0.0002) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = Math.tan(y) + (x - Math.tan(a));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -0.005:
		tmp = x + (math.tan(y) - math.tan(a))
	elif math.tan(a) <= 0.0002:
		tmp = (x + math.tan((y + z))) - a
	else:
		tmp = math.tan(y) + (x - math.tan(a))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -0.005)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	elseif (tan(a) <= 0.0002)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = Float64(tan(y) + Float64(x - tan(a)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -0.005)
		tmp = x + (tan(y) - tan(a));
	elseif (tan(a) <= 0.0002)
		tmp = (x + tan((y + z))) - a;
	else
		tmp = tan(y) + (x - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -0.005], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 0.0002], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], N[(N[Tan[y], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.0050000000000000001

   1. Initial program 81.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 62.0%

      \[\leadsto \color{blue}{\left(x + \frac{\sin y}{\cos y}\right) - \frac{\sin a}{\cos a}} \]
   3. Step-by-step derivation

      1. tan-quot 62.1%

         \[\leadsto \left(x + \color{blue}{\tan y}\right) - \frac{\sin a}{\cos a} \]

      2. tan-quot 62.1%

         \[\leadsto \left(x + \tan y\right) - \color{blue}{\tan a} \]

      3. associate--l+ 62.2%

         \[\leadsto \color{blue}{x + \left(\tan y - \tan a\right)} \]

   4. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{x + \left(\tan y - \tan a\right)} \]

   if -0.0050000000000000001 < (tan.f64 a) < 2.0000000000000001e-4

   1. Initial program 78.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Step-by-step derivation

      1. associate-+r- 78.8%

         \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

      2. +-commutative 78.8%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

      3. associate--l+ 78.8%

         \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x + -1 \cdot a\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \left(x + \color{blue}{\left(-a\right)}\right) \]

      2. unsub-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]

   6. Simplified 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]
   7. Step-by-step derivation

      1. associate-+r- 78.7%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right) - a} \]

   8. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right) - a} \]

   if 2.0000000000000001e-4 < (tan.f64 a)

   1. Initial program 73.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 58.4%

      \[\leadsto \color{blue}{\left(x + \frac{\sin y}{\cos y}\right) - \frac{\sin a}{\cos a}} \]
   3. Step-by-step derivation

      1. tan-quot 58.4%

         \[\leadsto \left(x + \color{blue}{\tan y}\right) - \frac{\sin a}{\cos a} \]

      2. tan-quot 58.5%

         \[\leadsto \left(x + \tan y\right) - \color{blue}{\tan a} \]

      3. associate--l+ 58.5%

         \[\leadsto \color{blue}{x + \left(\tan y - \tan a\right)} \]

   4. Applied egg-rr 58.5%

      \[\leadsto \color{blue}{x + \left(\tan y - \tan a\right)} \]
   5. Step-by-step derivation

      1. associate-+r- 58.5%

         \[\leadsto \color{blue}{\left(x + \tan y\right) - \tan a} \]

      2. +-commutative 58.5%

         \[\leadsto \color{blue}{\left(\tan y + x\right)} - \tan a \]

      3. associate--l+ 58.5%

         \[\leadsto \color{blue}{\tan y + \left(x - \tan a\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{\tan y + \left(x - \tan a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 0.0002:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;\tan y + \left(x - \tan a\right)\\ \end{array} \]

Alternative 6: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \mathsf{fma}\left(\tan z + \tan y, 1, x - \tan a\right) \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (fma (+ (tan z) (tan y)) 1.0 (- x (tan a))))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	return fma((tan(z) + tan(y)), 1.0, (x - tan(a)));
}

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	return fma(Float64(tan(z) + tan(y)), 1.0, Float64(x - tan(a)))
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] * 1.0 + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Step-by-step derivation

   1. associate-+r- 78.2%

      \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

   2. +-commutative 78.2%

      \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

   3. associate--l+ 78.2%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

3. Simplified 78.2%

   \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]
4. Step-by-step derivation

   1. add-cbrt-cube 77.8%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\sqrt[3]{\left(\left(x - \tan a\right) \cdot \left(x - \tan a\right)\right) \cdot \left(x - \tan a\right)}} \]

   2. pow3 77.8%

      \[\leadsto \tan \left(y + z\right) + \sqrt[3]{\color{blue}{{\left(x - \tan a\right)}^{3}}} \]

5. Applied egg-rr 77.8%

   \[\leadsto \tan \left(y + z\right) + \color{blue}{\sqrt[3]{{\left(x - \tan a\right)}^{3}}} \]
6. Step-by-step derivation

   1. tan-sum 99.0%

      \[\leadsto \color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} + \sqrt[3]{{\left(x - \tan a\right)}^{3}} \]

   2. rem-cbrt-cube 99.6%

      \[\leadsto \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \color{blue}{\left(x - \tan a\right)} \]

   3. div-inv 99.6%

      \[\leadsto \color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} + \left(x - \tan a\right) \]

   4. fma-def 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\tan y + \tan z, \frac{1}{1 - \tan y \cdot \tan z}, x - \tan a\right)} \]

   5. +-commutative 99.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\tan z + \tan y}, \frac{1}{1 - \tan y \cdot \tan z}, x - \tan a\right) \]

   6. *-commutative 99.6%

      \[\leadsto \mathsf{fma}\left(\tan z + \tan y, \frac{1}{1 - \color{blue}{\tan z \cdot \tan y}}, x - \tan a\right) \]

7. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\tan z + \tan y, \frac{1}{1 - \tan z \cdot \tan y}, x - \tan a\right)} \]

8. Taylor expanded in z around 0 78.7%

   \[\leadsto \mathsf{fma}\left(\tan z + \tan y, \frac{1}{\color{blue}{1}}, x - \tan a\right) \]

9. Final simplification 78.7%

   \[\leadsto \mathsf{fma}\left(\tan z + \tan y, 1, x - \tan a\right) \]

Alternative 7: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

2. Final simplification 78.3%

   \[\leadsto x + \left(\tan \left(y + z\right) - \tan a\right) \]

Alternative 8: 49.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.059:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.55) x (if (<= a 0.059) (+ (- x a) (tan (+ y z))) x)))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.55) {
		tmp = x;
	} else if (a <= 0.059) {
		tmp = (x - a) + tan((y + z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.55d0)) then
        tmp = x
    else if (a <= 0.059d0) then
        tmp = (x - a) + tan((y + z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.55) {
		tmp = x;
	} else if (a <= 0.059) {
		tmp = (x - a) + Math.tan((y + z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.55:
		tmp = x
	elif a <= 0.059:
		tmp = (x - a) + math.tan((y + z))
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.55)
		tmp = x;
	elseif (a <= 0.059)
		tmp = Float64(Float64(x - a) + tan(Float64(y + z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.55)
		tmp = x;
	elseif (a <= 0.059)
		tmp = (x - a) + tan((y + z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -1.55], x, If[LessEqual[a, 0.059], N[(N[(x - a), $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55000000000000004 or 0.058999999999999997 < a

   1. Initial program 77.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in x around inf 22.5%

      \[\leadsto \color{blue}{x} \]

   if -1.55000000000000004 < a < 0.058999999999999997

   1. Initial program 78.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Step-by-step derivation

      1. associate-+r- 78.8%

         \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

      2. +-commutative 78.8%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

      3. associate--l+ 78.8%

         \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x + -1 \cdot a\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \left(x + \color{blue}{\left(-a\right)}\right) \]

      2. unsub-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]

   6. Simplified 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.059:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 49.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.059:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -2.2) x (if (<= a 0.059) (- (+ x (tan (+ y z))) a) x)))

C

assert(y < z);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.2) {
		tmp = x;
	} else if (a <= 0.059) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.2d0)) then
        tmp = x
    else if (a <= 0.059d0) then
        tmp = (x + tan((y + z))) - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.2) {
		tmp = x;
	} else if (a <= 0.059) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	tmp = 0
	if a <= -2.2:
		tmp = x
	elif a <= 0.059:
		tmp = (x + math.tan((y + z))) - a
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -2.2)
		tmp = x;
	elseif (a <= 0.059)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -2.2)
		tmp = x;
	elseif (a <= 0.059)
		tmp = (x + tan((y + z))) - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -2.2], x, If[LessEqual[a, 0.059], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2000000000000002 or 0.058999999999999997 < a

   1. Initial program 77.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in x around inf 22.5%

      \[\leadsto \color{blue}{x} \]

   if -2.2000000000000002 < a < 0.058999999999999997

   1. Initial program 78.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Step-by-step derivation

      1. associate-+r- 78.8%

         \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]

      2. +-commutative 78.8%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right)} - \tan a \]

      3. associate--l+ 78.8%

         \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + \left(x - \tan a\right)} \]

   4. Taylor expanded in a around 0 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x + -1 \cdot a\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \left(x + \color{blue}{\left(-a\right)}\right) \]

      2. unsub-neg 78.7%

         \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]

   6. Simplified 78.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\left(x - a\right)} \]
   7. Step-by-step derivation

      1. associate-+r- 78.7%

         \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right) - a} \]

   8. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\left(\tan \left(y + z\right) + x\right) - a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.059:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 31.5% accurate, 207.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 x)

C

assert(y < z);
double code(double x, double y, double z, double a) {
	return x;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x
end function

Java

assert y < z;
public static double code(double x, double y, double z, double a) {
	return x;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, a):
	return x

Julia

y, z = sort([y, z])
function code(x, y, z, a)
	return x
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, a)
	tmp = x;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := x

Derivation

1. Initial program 78.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

2. Taylor expanded in x around inf 29.7%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 29.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023278 
(FPCore (x y z a)
  :name "tan-example (used to crash)"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))